Henniart, Guy The local Langlands conjecture for \(\mathrm{GL}(p)\). (La conjecture de Langlands locale pour \(\mathrm{GL}(p)\).) (French) Zbl 0564.12020 C. R. Acad. Sci., Paris, Sér. I 299, 73-76 (1984). Let \(F\) be a local field of residual characteristic \(p\). The note announces the existence of a Langlands correspondence between equivalence classes of p-dimensional semisimple representations of the Weil-Deligne group of \(F\) and irreducible admissible representations of \(\mathrm{GL}(p,F)\). The proof is sketched. Almost the same work has been done by Ph. Kutzko and A. Moy, see their paper [Ann. Math. (2) 121, 495–517 (1985; Zbl 0609.12017)]. Reviewer: J. G. M. Mars Cited in 13 Documents MSC: 11S37 Langlands-Weil conjectures, nonabelian class field theory 22E50 Representations of Lie and linear algebraic groups over local fields Keywords:local Langlands conjecture; base change; epsilon-factor; local field; Langlands correspondence; semisimple representations of the Weil- Deligne group; irreducible admissible representations Citations:Zbl 0609.12017 PDFBibTeX XMLCite \textit{G. Henniart}, C. R. Acad. Sci., Paris, Sér. I 299, 73--76 (1984; Zbl 0564.12020)